The BCE's initial proposals constitute yet another 'botch' and do not properly take into account the real links between these areas, the routes of the London Overground line and Southeastern railway line in particular, or the fact that 51 years on from the creation of the current London boroughs, the old districts they replaced still have a sense of identity and this is respected when local ward boundaries are drawn (usually).
Contrary to what is first believed, Lewisham Deptford can be saved if the 'Lewisham' parts are moved to other constituencies, leaving the four 'Deptford' wards behind, and there is no need to combine Peckham with Lewisham. The Crystal Palace community within Bromley should not be split either, as the BCE proposes, but should be kept whole when combined with the rest of Beckenham (which has parts of Bromley in it, but this is easily fixed). As for the rest of Lewisham, recreating the old Lewisham West constituency is not a problem as long as it extends to absorb the Lewisham wards formerly in Deptford, but no part of the actual community of Deptford.
Southwark and Bexley are trickier due to ward size issue, especially in the Bermondsey part of Southwark where substantial developments have taken place. Instead of being combined with Lewisham, Peckham should be combined with Dulwich, just as part of it was before 1997. This does however result in the splitting of Bermondsey & Old Southwark, with Southwark joining Camberwell and Bermondsey being paired with Deptford, just as the aborted 2013 review recommended. With many under-sized constituencies in the eastern part of South East London, one or two prominent splits are inevitable.
My alternative proposals for South East London constituencies in the 2018 review are:
Dulwich & Peckham succeeds Camberwell & Peckham.
Camberwell & Southwark succeeds Bermondsey & Old Southwark in practice.
Bermondsey & Deptford succeeds Lewisham Deptford in practice.
Lewisham West succeeds Lewisham West & Penge (Penge itself is moved back to Beckenham).
Lewisham East & Greenwich succeeds Lewisham East.
Woolwich succeeds Greenwich & Woolwich.
Erith & Crayford succeeds Bexleyheath & Crayford.
Bexleyheath & Sidcup succeeds Old Bexley & Sidcup.
The final part in the London section of my series of alternative proposals takes us to South London (Lambeth, Wandsworth, Merton, Sutton, and Croydon).